this question is from Schweser 08’notes book4 P29 the NPV profiles of 2 projects will intersect if the projects have different: A.sizes and different lives B.IRRs and different lives C. IRRs and different costs of capital D.sizes and different costs of capital answer is A. anyone can explain why?

NPV Profile is basically a graph of NPV vs. IRR across projects. NPV=Sum CF of the project when IRR=0. By definition. When two projects have different lives, and different sizes – the lines have more of a chance of intersecting. Again, would recommend you read the Corp Fin material (at least glance thro’ the topic) on the CFAI text. You would also need to be critically aware of what the NPV Crossover means, and the interaction below the crossover point and above the Crossover point, because that is testable material. CP

why not is B? in the sample, 2 projects do have different IRRs.

that’s an interesting question. I’d say, NPV profiles would intersect if the project with a higher IRR has lower sum of undiscounted cash flows then the project with a lower IRR. Long project typically has larger sum of undiscounted cash flows and smaller IRR. -> A

maratikus Wrote: ------------------------------------------------------- > that’s an interesting question. I’d say, NPV > profiles would intersect if the project with a > higher IRR has lower sum of undiscounted cash > flows then the project with a lower IRR. Long > project typically has larger sum of undiscounted > cash flows and smaller IRR. -> A --------------------------------------------------- Maratikus, in your analysis, you also agreed there are different IRR.

just to add some (hopefully accurate) discussion to cpk and maratikus’ true-to-form good points: annex, you’re correct that when two NPV profiles cross they have different IRRs, but the presence of different IRRs when coupled with different project lives doesn’t assure the profiles actually will cross… If two projects are the same size but have different lives, shouldn’t they originate from the same point on the y-axis (i.e. be equal when the cost of capital is zero)? So if this is true, these profiles can’t ever cross and this situation looks a lot like Answer B (i.e. different lives, different IRRs) Now let’s try out two projects with equal lives but different sizes. They must originate from different points on the y-axis (after all, they’re different sizes and must have different NPVs if they’re not discounted at all). So assuming I’m right (which is a stretch, as we know), can you think of a way to cross these two profiles? The larger project will have a larger IRR and the smaller one will have a smaller IRR, right? Won’t these profiles move basically parallel down towards the x-axis? Granted, I haven’t thoroughly considered messing around with the timing of cash flows. It seems like you’d have to push all the cash flows from the larger project to the very end (to minimize IRR) and have a lot of early cash flow for the smaller project, with a small amount at the very end (to maximize IRR) and maybe get these profiles to cross… So but if you have two projects with different sizes and different lives, a larger (and likely longer) project starts out higher on the y-axis and slopes more steeply towards the x-axis while the smaller (likely shorter) project starts lower on the y-axis and has a flatter slope towards the x-axis… viola! Anyway, that’s my $0.02 for now.

annex, The other thing to remember is IRR is defined by the size of the project and the life of the project. Size --> defines the Cash flows. Life --> defines the time line for the cash flows. Since you use the above two and calculate the IRR --> any choice with an IRR in it, would be a wrong choice. A.sizes and different lives B.IRRs and different lives but a higher Cost of capital would lead to a lower NPV, and vice versa. CP

hiredguns1, great explanation. cpk123, it seems like there is some kind of miscommunication here. I don’t quite understand your explanation of why if we have an IRR, that’s necessarily a bad choice. NPV profile is a function of NPV(discount rate). The problem is asking whether a discount rate exists such that NPV1(discount rate + epsilon) > NPV2(discountrate + epsilon) and NPV1(discount rate - epsilon) < NPV2(discountrate - epsilon).

Maratikus, What I am trying to say is: Size of the Cashflows, and their distribution over the Life of the project go to identify the IRR component. And since the NPV Crossover chart is linking NPV and IRR together – and IRR is identified by Cashflows and Life – you would be ending up with a “circularity” argument if you used IRR in the mix. Which came first – Cashflows and Life – which defines IRR and not the other way around. That is why I am saying IRR would be a wrong choice, and hence two answers get eliminated. CP

Do you mean that NPV provile is linking NPV and IRR as NPV(IRR) = 0?

NPV with an IRR of 0 = Sum (CashFlows for the project) NPV = 0 @ IRR for the Project. Key thing to remember NPV Profiles of two projects intersect because of a difference in the timing of the Cashflows. CP

cpk123, I separate NPV, IRR and discount rate. I’m not comfortable saying that NPV with an IRR of 0 is equal to the sum of undiscounted cash flows because IRR is a fixed number that only depends on the cash flows and their timing. It doesn’t depend on discount rate, NPV, etc. When discount rate is equal to 0, NPV = sum of undiscounted cash flows. NPV is a function of the cash flows, their timing and the discount rate. When discount rate is equal to IRR, NPV = 0 NPV profile is a function of the discount rate, not IRR which is fixed for a project.

accepted. I just looked up the book again. I was under the mistaken impression that NPV Profile was NPV against IRR – which was why I went off completely on a tangent. Sorry about that. CP

no worries, cpk123. I’m sure you will correct me many times in the next couple of months.

thanks for all of you. Try to summry some points: project’s size decides the starting point from Y axis(NPV) when cost of capital=0. 2 projects must have different sizes in order to crossover, if not will start from same point of Y axis. and size is sum of all undiscounted cashflow,no matter when or how big or small. Live of project is to define when and how cashflow will come; in the NPV profile graph, it defines how NPV slope steeply to X axis (cost of capital). same lives means 2 projects’ NPV line are parallel, won’t crossover. IRR is calculated based on cashflow’s size and timing(lives). it is not essential to decide 2 projects profiles will intersect.